many brand name machines use airguides and chassis fans to do all the cooling (barring the PSU) ... They'll have a fanless CPU heatsink, a big fan on the case and will rely on the airflow thru the chassis with the side on to properly cool everything. When running with the side off, things can often get uncomfortably hot due to the lack of airflow in the right places. For instance it might well cool the CPU, but doesnt then flow any air over the hard disks or ram etc.
Yes, I've conceded that if there are case/chassis fans, then one does need the side on the case for the cooling to work properly. I guess my experience is at the lower end of the market - I've had umpteen PCs (and still have many of them, working!), nearly all "brand name" ones, but have never had one with any case fans. In the absence of such fans, I'm not convinced that having the side off does any great harm - although I suppose that the PSU fan may 'suck' air over various things (like the hard disks and RAM you mention) if the side is on.
Kind Regards, John